Well, yes, cat allergies can lead to pink eyes. As we know that pink eye is a bacterial infection caused by Staphylococcus or Streptococcus bacteria. Also, some irritants, pollutes can lead to pink eyes. At that moment, your eyes will red, even bloodshot. So when you suffer cat allergies, it is possible to have pink eyes, because of the irritants. By the way, it is very contagious. Anyway, just be careful about it.
Well, so sorry to know that you are allergic to cats. Anyway, the cat is one of the most lovely animals on the planet. Anyway, as long as you are allergic to them, sometimes the cat allergy could give rise to some reactions such as watery eyes,red eyes, sneeze all the time. What you should do is to stay away from cats and take more exercise to improve your immune system.